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FRM Part II · FRM Exam Part II · Market-Driven Scenarios: An Approach for Plausible Scenario Construction

Assume factors X and Y are jointly normal with zero means. Factor X has daily volatility of 2.0%, factor Y has daily volatility of 3.0%, and their correlation is 0.60. A scenario sets the shock to X at -4.0% (a 2-standard-deviation fall). What is the conditional expected shock to Y?

The conditional expected shock to Y is -3.6%. With joint normality it equals correlation times the volatility ratio times X's shock: 0.60 × (3/2) × (-4%) = -3.6%. Equivalently, X is down 2 standard deviations, so Y is expected down 1.2 of its own standard deviations.

  1. A-3.6%Correct
  2. B-6.0%
  3. C-2.4%
  4. D-4.0%

Explanation

Conditional expectation E[Y|X=x] = rho × (sigma_Y/sigma_X) × x = 0.60 × (3/2) × (-4%) = -3.6%. Check: X is -2 sigma, so Y is expected at 0.6 × -2 = -1.2 sigma = -1.2 × 3% = -3.6%. The -2.4% option omits the volatility ratio (0.6 × -4%).

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